Oh homework number 3, ch.5-14, there are 2 masses connected by a light spring on a frictionless table. It gives the acceleration fo one block. Shouldn't the accelerations be the same for both? Or is it because it is a spring and not a rope or string?
You should draw a free bosy diagram for each of the blocks and for the spring (assume it has some very small but non-zero mass.). When you do this, you should find that the force of the spring on the two blocks must be equal in magnitude but mutually opposite in direction. So, to answer your first question, the magnitude of the accelerations of the two blocks will be the same but the directions of the acceleration vectors are antiparallel. If the spring were replaced with a rope (or a string) then the free body diagrams (at some initial instant) would be unchanged; however, the long-time behavior of the system would be very different.